PROBLEM 2E

Assume that the weight X in ounces of a “10- ounce” box of cornflakes is N(μ, 0.03). Let X1,X2, . . . ,Xn be a random sample from this distribution.

(a) To test the hypothesis H0: μ ≥ 10.35 against the alternative hypothesis H1: μ < 10.35, what is the critical region of size α = 0.05 specified by the likelihood ratio test criterion? Hint: Note that if μ ≥ 10.35 and

(b) If a random sample of n = 50 boxes yielded a sample mean of is H0 rejected? Hint: Find the critical value zα when H0 is true by taking μ = 10.35, which is the extreme value in μ ≥ 10.35.

(c) What is the p-value of this test?

GenBus306Session9: RandomVariables Forcaseupdates Assume15%telephonebookings Nowthatweknowaboutprobability,howdowemakedecisionsinvolvingrisk Tomakeadecision,weneedtoknowpossibleoutcomes(radonvariables)and probabilitiesofoutcomes(distributions) Arandomvariable(canbecontinuousordiscrete)associatesanumericvaluewitheach possiblerandomoutcome...